A Variational Model for Historical Systems of Rural Settlement (on the Example of the Derevskaya Pyatina on the Territory of Novgorod)

Abstract

The research subject of this article is the mathematical modeling of the process of spatial settlement among medieval rural populations. Due to the heterogeneous features of land in different regions, the distribution of populations is not uniform. Along with the system of ordinary settlements, the presented model examines the system of the centers serving them. As such, there are settlements that have concentrated on themselves the functions of serving the entire surrounding population (for example, tribute collection centers or parish centers). The model assumes that the distribution of the system of centers is not uniform. The aim of the developed model is to describe the laws of such settlement systems. In order to achieve this goal, an innovative variational approach is developed, the essence of whichconsists in considering the process of historical settlement as a self-developing system, characterized by its parameters and needs. The use of the mathematical methods of variation calculations within the framework of this approach allowed the author to find the parameters of the existing systems for establishing centers and to quantitatively describe the relevant phenomena occurring within them. The testing of the proposed model is carried out on the basis of one rural settlement structure from the late 15th - early 16th centuries (Derevskaya Pyatina on the territory of Novgorod). A high degree of correspondence in the obtained theoretical results from empirical data allows the author to consider mathematical modeling as an adequate and convenient auxiliary tool for studying the process of historical settlement.